How did the 13th, 14th, and 15th Amendments support the Radical Republicans' goal for Reconstruction?

yes

explanation:

powers  are  denied  to the  national governmentin three distinct ways: some  powers, such as the  power  to levy duties on exports or prohibit the freedom of religion, speech, press, or assembly, are expressly  denied  to the  national government  in the  constitution.

they change the constitution.